Exact solutions for stimulated emissions by external sources

The exact solutions for transition amplitudes are derived forstimulated emissions by external sources. More precisely, we obtain the exact expressions for transition amplitudes for the emission of an arbitrary number of particles by the sources when some particles are already present, in the process,prior to the switching on of the external sources. The solutions are given for an arbitrary number of particles with arbitrary configurations (of momenta, spin, etc.) and for particles of spin-0, spin-1/2, massive and massless (photons) spin-1 particles, and massless (gravitons) spin-2 particles. Applications are given as illustrations to the process Ø anything, and, in quantum electrodynamics, to the process e ⁺e^–+ any photons, in thepresence of external sources, where a (virtual) photon decays into the paire ⁺e^–.     

Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

Differentiable structure for direct limit groups

A direct limit of (finite-dimensional) Lie groups has Lie algebra and exponential map exp _G : gG. BothG and g carry natural topologies.G is a topological group, and g is a topological Lie algebra with a natural structure of real analytic manifold. In this Letter, we show how a special growth condition, natural in certain physical settings and satisfied by the usual direct limits of classical groups, ensures thatG carries an analytic group structure such that exp _G is a diffeomorphism from a certain open neighborhood of 0g onto an open neighborhood of 1 _G G. In the course of the argument, one sees that the structure sheaf for this analytic group structure coincides with the direct limit C (G ) of the sheaves of germs of analytic functions on theG .L.N. partially supported by a University of California Dissertation Year Fellowship.E.R.C. partially supported by N.S.F. Grant DMS 89 09432.J.A.W. partially supported by N.S.F. Grant DMS 88 05816.     

Bohr's discussion of the fourth uncertainty relation revisited

Bohr's 1930 derivation of the uncertainty relation c ² m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c ² m th, avoiding Treder's 1971 objection.     

Cross-section asymmetry for the reactions γd →pn, γd → π0 d by linearly polarized photons in the energy rangeE γ = 0·4 – 0·8 GeV

The beam asymmetryB has been measured for the reactiond pn in the energy rangeE = 0·4 ÷ 0·8 GeV and angles _p ^cm = 45 ÷ 95° and ford ⁰d at energiesE =0·5, 0·6, 0·7 GeV and angle ^cm = 130°. The results obtained are compared to existing theoretical predictions which take into account the possible contribution of dibaryon resonances.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Weyl's geometry and physics

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using standard vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter . For =0 one has the electromagnetic field. For <0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the missing mass of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution.     

Deposition kinetics of the γ′ phase in N36T2YU2 steel

Electron microscopy is reported for the deposition in this steel; quantitative results are given on the particle size of the phase deposited during a continuous and uninterrupted decomposition. The deposition of the phase occurs in one stage, while the two stages in the variation in the mechanical properties arise from features of the interaction of dislocations with the phase particles. There appears to be only a small energy barrier to the generation of phase particles. Spherulites are formed in regions of interrupted decomposition. The effects of quenching temperature on the deposition mechanism are discussed.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 41–45, March, 1973.     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

Spectroscopic properties of the photoproducts of pyridoxal-5′-P irradiation: Catalytic site recognition of ribonuclease A

Photoproducts of pyridoxal-5-P, i.e., 4-pyridoxic-5-P and bis-pyridoxal-5-P, have been studied by spectroscopic methods. The spectroscopic properties of bis-pyridoxal-5-P (bis-PLP) resemble those of pyridoxal-5-P (PLP) under similar experimental conditions. The coupling of methylen hydrogens to the phosphorus atom has been shown by NMR spectroscopy. The singlet in the³¹P-NMR spectra and the triplet in¹H-undecoupled experiments confirm the presence of the phosphate group in the 5 position of the structure of the vitamin. The effect of pH and solvent composition on the relative distribution of species of bis-pyridoxine-5-P (bis-PNP) has been investigated by absorption and fluorescence spectroscopy. The acid-base dissociation of the phosphate group is easily detected by emission spectroscopy. Bis-PNP and bis-PLP bind to the enzyme RNase A and they behave as competitive inhibitors with respect to the substrate cytidine-2-3-cyclic phosphate. The natural forms of vitamin B₆, pyridoxine, and pyridoxine-5-P have no effect on the catalytic activity of the protein. Experimental evidence derived from fluorescence and inhibition experiments is consistent with the hypothesis that bis-PNP recognizes the catalytic site of RNase A.     

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VI_h cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (–1) is imposed in the particular case of Bianchi VI₀ string models. Various physical and kinematical properties of the models are discussed.     

O(5)×U(1) electroweak gauge theory and the relevance of the Cabibbo angle inCP violation inK decays

Some of the relevant mathematics ofO(5)×U(1) electroweak gauge theory is briefly sketched. TheO(5)×U(1) model is presented. To facilitate the discussion ofCP violation inK decays, the relevant Lagrangian is given in several alternative forms. It is shown that in theCP-violating part of the Lagrangian, by a redefinition of quark phases, the coupling of theCP eigenstatesK ₁ andK ₂ cannot be broken. However, if the Cabibbo angle were not present, the statesK ₁ andK ₂ would decouple and the theory would becomeCP-invariant. Such a result was also reported by Deshpandeet al., working with a different formalism. Relating the mixing parameters and to the parameters ₁ and ₂, it is shown that when ₁= ₂=, reduces to the usualCP-violating andCPT-conserving parameter.     

On practical calculations with reflection curves for perfect crystals

The application of the Prins function for practical calculations is rather laborious. In the present article it is shown by analysis of some of the properties of this function that in most experiments with perfect crystals one may use functions of a much simpler form. Such a function is proposed, its use is shown on some examples, a method of simplified calculation of the fundamental constants of the Prins function is given, and finally some numerical examples are added as illustration.

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. , . , , , , .

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These curves will be hereafter called Prins functions.

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The author is greatly indebted to M. Malkovská for the experimental data in Chapter VI. C and to V. Horáková for numerical computations of the integrals in Appendix 2.     

Anticommutative Electric and Magnetic Charges, and the Monopole Question

The monopole question is treated anew in the light of a recent, strictly covariant,extended formulation of fermion quantum field theory naturally including alsoa pseudoscalar variety of conserved charges. The essential novelty lies in theresulting quantum property of anticommutivity between scalar and pseudoscalarcharge varieties, which should in particular apply to electric and magnetic charges.As an immediate outcome, there should no longer be any (Dirac-like) quantizationcondition relating these charges and binding the magnetic elementary charge tohave a very great strength. A generalized Lagrangian approach to the monopoleproblem is made truly viable, leading to two independent local gauge couplingswhich are separately generated by the electric and magnetic elementary chargesand are not allowed to interfere. This would prevent electric and magneticmonopoles from mutually interacting and would particularly account for theabsence of magnetic sources in ordinary electromagnetism. Within such aframework, an electric charge eigenstate with a nonzero eigenvalue is bound tohave a null magnetic charge expectation value, and the magnetic dipole momentof an electrically charged point fermion may actually be seen as resulting fromthe additional internal presence of a single magnetic charge subjected to a maximaluncertainty in sign. An easy estimate makes it allowable to assign to this chargea strength just equal to that of the partner electric charge. Such a conjecture leadsto a dual model of a charged point fermion where the electric and magneticroles can well be interchanged with no observable effects. In the associatedformalism, duality symmetry is already included without the need to appeal toany missing electromagnetic phenomenology to be discovered.     

Compact recording of information by the holographic method

Conclusions For holography using a convergent subject beam arrangement, the effect associated with increased extrafocal information density is most pronounced when the parameter 2ac/F is small. This relationship between the object parameters (a and c) and the characteristics of the holographic system (, F) is encountered most frequently in problems of microfilming (ac) and radar imaging (ac,a ²/F is small). It is only in the case 2acF99 with an accuracy of not worse than 1%, that we can assert that the sizes of the minimal Fourier holograms will coincide.Gorkii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 4, pp. 449–457, April, 1979.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Nonlinear approach to electrodynamics

A nonlinear approach to electrodynamics is reviewed. On imposing a nonlinear constraintA A = – ², together with the usual gauge-invariant electromagnetic field Lagrangian, it is found that the resulting equations of motion have, besides the photon, a static spherically symmetric extended solution which may be regarded as a charged particle. A magnetic dipole moment (spin) can also arise as a solution of the equations of motion if, as expected, it is treated as a first-order quantum effect. In the limit for small quantum fields and pointlike charged particles, the quantum mechanical equivalence of the approach with the usual Lagrangian formulation of the electromagnetic interaction of a charged scalar field is heuristically shown. Moreover the possibility of constructing charged fermion fields from the solution having both a charge and a magnetic moment is illustrated. In such an approach the photon is associated with the spontaneous breaking of Lorentz symmetry, and the emission of soft photons does not exhibit any infrared divergences.     

Groundstate properties of a generalized VBS-model

We study a generalized q-deformed VBS-model. This is a spin-1 quantum antiferromagnet with nearest neighbour interaction on a linear chain. The exact grounstate is determined in the form of a matrix-product of individual site-contributions. All relevant groundstate properties are calculated. The groundstate is unique, it has a finite gap to the excitations, and correlations decay exponentially. Thus the model has all the properties described by Haldane to be generic for certain quantum antiferromagnets with integral spin.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Nonperturbative construction of nonrenormalizable models of quantum field theory in four-dimensional space-time

The report presents the construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions _I()= d(ge): exp : in four-dimensional space-time. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps theSO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.Supported in part by NSF Grant No INT 73-20002 A 01 (formerly GF-41958).The author would like to thank Professors T.Balaban, J.Fröhlich and A.Uhlmann for interesting discussions and valuable suggestions. He would also like to express his sincere thanks to Professor J.Niederle for the very kind hospitality extended to him during his stay at the Symposium on Mathematical Methods in the Theory of Elementary Particles in Liblice Castle.